The present invention pertains to microlithography (projection-transfer of a pattern, defined by a reticle, onto a sensitive substrate) using an energy beam such as a charged particle beam (e.g., electron beam or ion beam). Microlithography in general is a key process used in the manufacture of microelectronic devices such as integrated circuits, displays, and the like. More specifically, the invention pertains to methods for determining proximity effects encountered with certain microlithography techniques, especially charged-particle-beam (CPB) microlithography. The methods involve determinations of cumulative exposure energy (exposure dose) at specific loci on a sensitive substrate. The results of such determinations are used for, inter alia, designing reticles that are less subject to proximity effects during use.
All conventional wafer-processing methods include at least one microlithography step, in which a pattern, defined on a mask or reticle, is transferred onto a sensitive substrate such as a semiconductor wafer. Typically, multiple xe2x80x9cchipsxe2x80x9d are formed on each wafer, and multiple microlithography steps are performed to form various patterned layers of the chips. As an energy medium for making the pattern transfer, a beam of electromagnetic radiation (e.g., light, X-rays) or of charged particles (e.g., electron beam, ion beam) is used. To be imprinted with the pattern, the substrate is coated with a suitable xe2x80x9cresist.xe2x80x9d With a xe2x80x9cpositivexe2x80x9d resist, regions that receive a cumulative exposure energy (dose) exceeding a threshold value are removed by developing the resist. With a xe2x80x9cnegativexe2x80x9d resist, regions that receive a cumulative exposure dose exceeding a threshold value are left on the wafer after development. Hence, in order to form a pattern properly on the substrate, it usually is necessary to calculate whether the cumulative exposure dose at each region of the substrate is higher than the specified threshold value. It also is necessary to configure the reticle so that the respective shapes of the regions where energy accumulates above the threshold value will form pattern elements having the intended profiles.
In charged-particle-beam (CPB) microlithography, xe2x80x9cproximity effectsxe2x80x9d frequently are encountered, in which the respective doses of exposure energy received at any of various loci on the wafer surface vary according to the respective distribution and configuration of pattern elements in the vicinity of the loci. I.e., the distribution and configuration of nearby pattern elements affect the manner in which charged particles of the beam are scattered as they encounter the substrate. Scattered charged particles can cause unintentional development of nearby regions of the resist in various ways, resulting in pattern elements being formed on the substrate having profiles that deviate substantially from the intended profiles of the elements. I.e., the profiles of the pattern elements as formed on the wafer unintentionally have different profiles than the corresponding elements as defined on the reticle.
In optical microlithography, proximity effects as summarized above generally do not occur. However, errors in the pattern as transferred to the substrate can occur due to light diffraction. Hence, in both optical and CPB microlithography, unavoidable differences can arise between the shapes of pattern elements as defined on the reticle versus the shapes of corresponding pattern elements as formed on the substrate.
Various methods have been considered for solving this problem. The methods generally involve changing and adjusting localized cumulative amounts of radiation dose received at the substrate so as to obtain the desired distribution of cumulative exposure energy at the surface of the substrate. For example, certain methods involve localized deformation of certain pattern elements as defined on the reticle.
A conventional method for calculating local cumulative exposure dose, leading to corresponding deformations of pattern elements as defined on the reticle to correct proximity effects in CPB microlithography, is discussed below, referring to FIGS. 20(a)-20(c). In FIG. 20(a), item 101 is a pattern element having a profile that is to be transferred to the substrate with minimal profile change. For convenience, the transfer magnification is unity. The edge of the pattern element 101 is divided into N segments S1-SN as shown in FIG. 20(b). The element as defined on the reticle is deformed deliberately by moving each of these segments a tiny amount in a direction perpendicular to the direction in which the edge of the segment extends. This is shown in FIG. 20(c), which depicts a magnified view of a portion of the pattern element 101 after moving certain segments. Specifically, FIG. 20(c) shows segments S1, S2, and SN. The desired outline of the pattern element to be formed on the substrate is denoted by the line 102. In FIG. 20(c), segments SN and S2 have been moved inward relative to the line 102 (thereby forming xe2x80x9cindentsxe2x80x9d), and the segment S1is moved outward (thereby forming a xe2x80x9cprojectionxe2x80x9d). A1, A2, AN denote respective points on the line 102 corresponding to centers of the respective edges ofxe2x80x9cpre-movexe2x80x9d segments S1, S2, SN. The points A1, A2, AN are points at which evaluations of cumulative exposure dose are made.
Referring further to FIG. 20(c), D1, D2, and DN are respective vectors indicating the magnitude and direction of movement of the edge of each respective segment S1, S2, SN. A respective vector D1-DN is assumed for each segment S1-SN in this manner, and the change in cumulative exposure dose occurring at each evaluation point A1-AN is calculated in accordance with the change in position of the edge of each segment according to the respective vector. That is, cumulative exposure energy (dose) is changed at each evaluation point Ai (i=1, 2, . . . , N) by moving the edge of the respective segment S1-SN according to the respective vector Dj (j=1, 2, . . . , N), and the change in cumulative exposure dose received at each evaluation point Ai (i=1, 2, . . . , N) can be determined from the respective vector.
Before actually moving each segment S1-SN, the cumulative exposure dose that would be received by the entire respective pattern element (e.g. as shown in FIG. 20(a)) after moving the segments is determined. Desirably, the total exposure dose received by the element after moving the segments is unchanged from the total exposure dose that otherwise would be received by the pattern element before moving the segments. Hence, for each element, the vectors Dj (j=1, 2, . . . , N) are re-determined in an iterative manner as required until the total exposure dose received by all the evaluation points Ai (i=1, 2, . . . , N) of the element is equal to the total that otherwise would be obtained if the respective pattern element were unchanged from that shown in FIG. 20(a).
In the method summarized above, the evaluation points Ai (i=1, 2, . . . , N) are positioned on the sensitive substrate to correspond to the center points of each xe2x80x9cpre-movexe2x80x9d segment S1-SN. Alternatively, the distribution of cumulative exposure dose may be evaluated along respective lines intersecting each segment at an angle, as described in U.S. Pat. No. 5,698,859, incorporated herein by reference. For example, the distribution of cumulative exposure dose can be evaluated along a line 103 perpendicularly intersecting segment S2 (FIG. 20(c)).
FIGS. 21(a)-21(b) show a second conventional method for calculating cumulative exposure dose, termed a xe2x80x9crepresentative figurexe2x80x9d method. This method achieves simplification of pattern-element figures by reducing the number of pattern-element figures referred to for calculating cumulative exposure energy (dose). I.e., the complex and fine pattern-element figures of, e.g., an LSI pattern are replaced (for analysis purposes) with simple figures each having xe2x80x9ccoarsexe2x80x9d pattern information that is the same as that of the original pattern-element figures in individual small regions of the pattern. For ease of discussion, the magnification of the image as formed on the substrate, relative to the pattern as formed on the reticle, is unity. In FIG. 21(a) xe2x80x9cPxe2x80x9d is a point at which cumulative exposure dose is calculated, xe2x80x9cFxe2x80x9d is a pattern element, and xe2x80x9c101xe2x80x9d denotes a reference region referred to for calculating the cumulative exposure dose. Only the pattern elements in the region 101 are assumed to have any effect on the cumulative exposure dose at the point P. The region 101 is divided into small regions 102 of a suitable size. (In this example, the region 101 is divided vertically and horizontally three times each, for a total of nine small regions 102. In actual practice each region 101 is divided into many more small regions 102 than nine.)
The total pattern-element area and centroid of the respective pattern element(s) in each small region 102 are calculated for each small region 102. Then, as shown in FIG. 21(b), a respective simplified figure Fxe2x80x2 (known as a xe2x80x9crepresentative figurexe2x80x9d) is created for each small region 102. Note that each small region 102 has a single representative figure. Each simplified figure Fxe2x80x2 has the same total pattern-element area and centroid as determined for the actual pattern element(s) in the respective small region 102 that may or may not contain pattern elements.
When calculating the cumulative exposure dose for each small region 102, the calculation is performed for each representative figure Fxe2x80x2 instead of having to calculate the dose for each pattern element F in the small region 102 and summing them for each small region 102. To form the small regions 102, the reference region 101 simply is divided equally, horizontally and vertically, into equal-area small regions 102.
The disadvantage with the first conventional method summarized above is that, with N divided segments, calculations must be performed N2 times. Hence, as N increases, the number of calculations increases geometrically, and calculation time correspondingly increases.
With the second conventional method summarized above, as the size of the small regions 102 increases, each small region encompasses more respective pattern elements that are replaced, for analysis purposes, by a respective representative figure, and calculation speed increases. However, simply increasing the size of the small regions does not take into account data concerning the distribution of pattern elements inside each small region 102. Consequently, the accuracy of the determined value of cumulative exposure dose received by each small region is less than obtainable if the representative figure method were not used. Conversely, if the size of the small regions 102 were to be decreased, then the accuracy of the exposure-dose calculations would increase, but there would be little to no difference between the number of original pattern elements and the number of representative figures. Hence, the benefit of improving calculation speed is lost.
In view of the shortcomings of the prior art as summarized above, an object of the invention is to provide improved methods for calculating cumulative exposure dose (energy) of defined regions of a reticle pattern. The methods provide a calculation accuracy at least as good as conventional methods but can be performed faster so as to accommodate the increasing number and complexity of pattern elements in contemporary microelectronic-device patterns. Other objects are to provide proximity-effect calculation methods utilizing such methods, reticle-design methods including such proximity-effect calculation methods, and microelectronic-device-fabrication methods utilizing reticles manufactured using such reticle-design methods.
A first aspect of the invention is directed to methods for determining a cumulative dose of exposure energy received by exposed portions of the sensitive substrate, as used in a microlithography method in which a pattern defined on a reticle is transferred to a sensitive substrate using an energy beam. According to one embodiment of such a method, in a first-level region of the reticle defining multiple pattern elements with respect to which cumulative exposure dose is to be determined, the total cumulative dose for the region is set initially to zero. Also, an evaluation point is selected in the region at which cumulative exposure dose is to be calculated. The region is divided in a branching manner into a second level of subregions each having a respective reference point from which distance measurements concerning the subregion are to be taken.
If a subregion has a size parameter that, in a ratio to a distance between the respective reference point and the evaluation point, is greater than a specified value xcfx86, then the following sub-steps are performed: (1) the subregion is not subdivided, (2) the pattern elements located in the subregion are converted into at least one corresponding representative figure, (3) based on the representative figure(s) in the subregion, a contribution of the subregion to the cumulative dose of exposure energy at the evaluation point is calculated, and (4) the contribution is added to the total cumulative dose for the evaluation point in the region. If a subregion contains a number of pattern elements that is no greater than a specified number m, then the following sub-steps are performed: (1) the subregion is not subdivided, (2) the pattern element(s) in the subregion are regarded as their own respective representative figure(s), (3) based on the representative figure(s) in the subregion, a contribution of the subregion to the cumulative dose of exposure energy at the evaluation point is calculated, and (4) the contribution is added to the total cumulative dose for the evaluation point in the region. The two conditional steps noted above in this paragraph can be performed in either order. If a subregion does not satisfy either of these conditional steps, then the subregion is subdivided in a branching manner into a next-lower (e.g., third) level of subregions, wherein each next-lower-level subregion has a respective reference point from which distance measurements concerning the subregion are to be taken. Then, the steps described in this paragraph are repeated for each of the next-lower-level subregions. After exhaustively subdividing the region as summarized above, the resulting cumulative exposure dose is regarded as the cumulative exposure dose for the evaluation point in the region.
This embodiment differs from the conventional xe2x80x9crepresentative figurexe2x80x9d method, in which the subject region is divided into identically sized subregions regardless of any specific characteristics of the region or of the distribution of pattern elements in the region. In this embodiment, in contrast, a subregion located distantly from the evaluation point has relatively little effect on the distribution of the pattern portion in the region. Hence, the more distant subregion can be larger than subregions nearer to the evaluation point. In contrast, a subregion located near the evaluation point has a relatively large effect on the distribution of the pattern portion in the region. Hence, the nearer subregion typically is relatively small. These differently sized subregions result from application of branching division according to the invention.
In other words, a region to be evaluated is subdivided according to specified rules. In applying the rules, decisions are made on whether to further subdivide a subregion. If the decision is to subdivide, then the subdivision is conducted according to the specified rules to produce subregions at the next lower level. In this manner, the region is divided into a respective group of subregions that are hierarchically related to each other according to the branching structure that was created.
In this embodiment, the decision criterion for whether to subdivide a region (or subregion) is the ratio of a size parameter of the region (or subregion) to the distance between the evaluation point and a xe2x80x9creference pointxe2x80x9d for the region (or subregion). The xe2x80x9cevaluation pointxe2x80x9d is a selected point in the region where the cumulative dose of exposure energy in the region is to be calculated. The xe2x80x9creference pointxe2x80x9d for the region or subregion can be, e.g., the center of the respective region or subregion. Representative size parameters include: (a) the area of the region or subregion, (b) the length of a side of the region or subregion (especially if the region or subregion is a regular polygon such as a square, etc.), and (c) the circumference of the region or subregion. An alternative distance parameter is the maximum distance between the evaluation point and the subject subregion.
If a subregion has a size parameter that, in a ratio to the distance between the respective reference point and the evaluation point, is smaller than the specified value xcfx86, and if the number of pattern elements contained in the subject subregion is no greater than m, then the respective pattern element(s) is regarded as the corresponding representative figure. The contribution of the subject subregion to the cumulative exposure energy for the evaluation point in the region is calculated using the representative figure. The contribution is added to the cumulative exposure energy, and no further subdivision of the subregion occurs. If the number of pattern elements contained in the subject subregion is larger than m, then the subregion is further subdivided in a branching manner into the next-lower-level of constituent subregions.
The simplest value of the number xe2x80x9cmxe2x80x9d is unity (1), which is useful for any pattern arrangement or size. A value of m=1 also is desired from the perspective of ensuring calculation accuracy.
The simplest manner of converting the pattern portion contained within a subject subregion into one or more representative figures is to convert the portion into a single representative figure. An exemplary method of making such a conversion is described in Oogi et al., xe2x80x9cHigh-speed Convolution System for Real-time time Proximity Effect Correction,xe2x80x9d Jap. J. Appl Phys. 37:6779-6784 (1998). If a subregion contains multiple pattern elements, then the subregion can be subdivided further into lower-level subregions each containing no more than one pattern element. The individual pattern elements in the lower-level subregions can be converted into respective representative figures.
In making the decision on whether to subdivide a region or subregion, a similar result is obtained regardless of which is performed first: (1) determining whether the size parameter of the region or subregion, in a ratio to a distance between the respective reference point and the selected evaluation point, is greater than a specified value xcfx86, or (2) determining whether the number of pattern elements contained in the subject region or subregion is no greater than a less than or equal to a specified number m.
In this embodiment, the steps of subdividing a subject region or subregion and determining cumulative exposure dose are performed simultaneously. Hence, at the time that a region is subdivided exhaustively and converted as required to corresponding representative figures according to the invention, calculation of the cumulative dose of exposure energy also is completed. Conventionally, calculating a contribution to exposure dose made by a representative figure is performed using a xe2x80x9crepresentative figurexe2x80x9d method as described in, for example, U.S. Pat. No. 5,863,682, incorporated herein by reference.
In another embodiment of a method according to the invention, in a first-level region of the reticle defining multiple pattern elements with respect to which cumulative exposure dose is to be determined, a total cumulative dose for a selected evaluation point in the region is initialized to zero. The region is divided in a branching manner into one or more sublevels of subregions as required until each of the subregions thus formed contains a respective number of pattern elements no greater than a specified number m. Such branching division creates a branching structure of subregions from the first level to an nh level, wherein each subregion has a respective reference point from which distance measurements concerning the respective subregion are to be taken.
If a subregion in an ith (1xe2x89xa6ixe2x89xa6n) level has a size parameter that, in a ratio to a distance between the respective reference point and the evaluation point, is greater than a specified value xcfx86, then the following sub-steps are performed: (1) pattern elements located in the subject subregion are converted into at least one corresponding representative figure, (2) based on the representative figure(s) in the subject subregion, a contribution of the subject subregion to the cumulative exposure dose is calculated, and (3) without regard to any contributions possibly made by (i+1)th or other lower-level subregions of the subject subregion, the contribution of the subject subregion is added to the total cumulative dose for the region. If the subregion in the ith level contains a number of pattern elements that is no greater than a specified number m, then the following sub-steps are performed: (1) the pattern element(s) in the subject subregion is regarded as its own respective representative figure(s), (2) based on the representative figure(s) in the subject subregion, a contribution of the subject subregion to the cumulative exposure dose is calculated, and (3) the contribution of the subject subregion is added to the cumulative dose for the evaluation point in the region. The two conditional steps noted above in this paragraph can be performed in either order. If a subregion does not satisfy either of these conditional steps, then the conditional steps are repeated for (i+1)th-level subregions of the subject subregion.
After performing the above for all applicable subregions of the region, then the resulting cumulative exposure dose is regarded as the cumulative exposure dose for the evaluation point in the region.
In the first embodiment summarized above, subdivision of a region and calculation of cumulative exposure energy were performed simultaneously, subregion-by-subregion as the subregions were designated. In the second embodiment, in contrast, complete branching division of a region is performed, until the number of pattern elements contained in each subregion is no greater than m. After the complete branching structure of the region is determined, representative figures are created for the pattern element(s) in the subregions thus formed, and respective contributions of the representative figures are calculated. The respective contributions are calculated in the same manner as in the first embodiment. Hence, the end result of the second embodiment is the same as with the first embodiment.
In yet another embodiment of a method according to the invention, a region of the reticle is selected that defines multiple pattern elements with respect to which cumulative exposure dose is to be determined. In the region, an evaluation point is identified at which cumulative exposure dose in the region is to be calculated. The region is subdivided in a branching manner into one or more sublevels of subregions. Each subregion has a respective reference point from which distance measurements concerning the respective subregion are to be taken
If a subregion has a size parameter that, in a ratio to a distance between the respective reference point and the evaluation point, is greater than a specified value xcfx86, then the subject subregion is not further subdivided, and any pattern elements located in the subject subregion are converted into at least one corresponding representative figure. If the subregion contains a number of pattern elements that is no greater than a specified number m, then the subject subregion is not further subdivided, and the pattern element(s) in the subregion is regarded as its own respective representative figure. The two conditional steps noted above in this paragraph can be performed in either order. If a subregion does not satisfy either of these conditional steps, then the subject subregion is subdivided in a branching manner into a next-lower level of subregions. The conditional steps are repeated for each of the next-lower-level subregions. After the region has been subdivided exhaustively according to the above, respective contributions of exposure energy from each of the subregions to a cumulative exposure dose for the region are calculated. The resulting cumulative exposure dose is regarded as the cumulative exposure dose for the evaluation point in the region.
In the first embodiment summarized above, subdivision of a region and calculation of cumulative exposure energy were performed simultaneously, subregion-by-subregion as the subregions were designated. In the third embodiment summarized above, subdivision of the region and creation of representative figures are performed first. After the representative figures are created, the cumulative energy at the evaluation point is determined by combining the individual contributions from each of the respective subregions. Hence, the result of this embodiment is similar to the result of the first embodiment.
In yet another embodiment of a method according to the invention, a subject region is divided in a branching manner into one or more sublevels of subregions as required until each of the subregions thus formed contains a respective number of pattern elements no greater than a specified number m. Hence, a branching structure is created of subregions from the first level to an nth level. Each subregion has a respective reference point from which distance measurements concerning the respective subregion are to be taken.
If a subregion in an ith (1xe2x89xa6ixe2x89xa6n) level has a size parameter that, in a ratio to a distance between the respective reference point and the selected evaluation point, is greater than a specified value xcfx86, then any pattern elements located in the subject subregion are converted into at least one corresponding representative figure. However, respective representative figures for pattern elements located in any lower-level subdivisions of the subject subregion are not created. If the subregion contains a number of pattern elements that is no greater than a specified number m, then the pattern element(s) in the subregion is regarded as its own respective representative figure. However, again, respective representative figures for pattern elements located in any lower-level subdivisions of the subject subregion are not created. If a subregion does not satisfy either of these conditional steps, respective representative figures are created for respective pattern elements contained in (i+1)th-level subregions of the subject subregion. With respect to all subregions of the subject region from the first level to the nth level, the individual exposure-dose contributions from the representative figures in the subregions are summed to yield a cumulative exposure dose for the evaluation point in the region.
In yet another embodiment, the region is divided in a branching manner into one or more sublevels of subregions as required until each of the subregions thus formed contains a respective number of pattern elements no greater than a specified number m. Thus, a branching structure of subregions is created from the first level to an nth level. For each subregion thus formed, if the subject subregion contains a number of pattern elements that is no greater than a specified number m, then the pattern element(s) in the subject subregion is regarded as its own respective representative figure(s). If the subject subregion contains a number of pattern elements that is greater than the specified number m, then the pattern elements located in the subject subregion are converted into at least one corresponding representative figure.
For each subregion formed as summarized above, if the subject subregion has a size parameter that, in a ratio to a distance between the respective reference point and the selected evaluation point, is greater than a specified value xcfx86, then a contribution of the subject subregion to the cumulative exposure dose at the evaluation point is calculated without considering any contribution of lower-level subregions of the subject subregion to the cumulative exposure dose. If the subject subregion contains a number of pattern elements that is no greater than the specified number m, then a contribution of the respective representative figure(s) to the cumulative exposure dose at the evaluation point is calculated without considering any contribution of lower-level subregions of the subject subregion to the cumulative exposure dose. Either conditional step can be performed first. If a subregion does not satisfy either of the conditional steps, then, in the calculation of the respective contribution of the subject subregion to cumulative exposure dose, contributions of lower-level subregions of the subject subregion are included. The individual calculated exposure-dose contributions from all the subregions of the region are summed to yield a cumulative exposure dose for the evaluation point in the region.
In this method, as in other methods summarized above, branching division of the region is performed until the respective number of pattern elements included in any subregion is less than or equal to a specified number m. Meanwhile, representative figures are formed in all subregions, including subregions at lower levels in which, in other embodiments summarized above, representative figures were not determined. It would appear that this would require excessive calculation time. However, if a similarly configured subregion appears at multiple places, the cumulative energy calculation for the evaluation point can be performed once for such a subregion and the results of the calculation used wherever the subject subregion occurs. Thus, calculation time can be reduced substantially for certain patterns.
In any of the methods summarized above, if the number of pattern elements included in a subregion is less than or equal to 1, instead of regarding the respective pattern element as its own representative figure, the pattern element can be converted into a respective representative figure having a simpler profile than the respective pattern element.
In any of the methods summarized above, if the number of pattern elements included in a subregion is no greater than a specified number m, then the respective pattern element can be regarded as its own representative figure. Alternatively, the pattern element can be converted into a respective representative figure having a relatively simple profile and usable for making cumulative-dose calculations, thereby simplifying the calculations.
In any of the methods summarized above, a pattern element can be divided into a combination of a core portion (e.g., having a relatively simple shape) and secondary portions located outside the core portion. One or more of the secondary portions can include portions having a negative shape. A separate cumulative energy calculation can be performed for the core portion (using conventional methods), with cumulative energy calculations for the secondary portions being performed using any of the above-summarized methods according to the invention. A cumulative exposure dose for a pattern element is obtained simply by adding the energy calculated for the respective secondary portions to the energy calculated for the respective core portion. This method variation can provide a more accurate and rapid determination of the respective exposure-dose contribution of, for example, a single complex pattern element present in a subregion. I.e., because the core portion has a simple profile, its contribution to cumulative exposure dose can be determined easily using conventional methods, saving the method according to the invention for calculating the respective contributions from the secondary portions.
Any of the processes summarized above can be recorded on a suitable computer-readable medium to allow automation of the method under the control of a computer. More than one method can be programmed on the same medium.
The foregoing and additional features and advantages of the invention will be more readily apparent from the following detailed description, which proceeds with reference to the accompanying drawings.